An IQ modulator shapes and samples an input signal to generate a series of discrete sampled values. Each sampled value includes an in-phase (I) component and a quadrature (Q) component, collectively referred to as a sampled IQ value. An IQ trajectory is a path derived from discrete sampled IQ values sampled from the input signal. The sampled IQ values are plotted on an IQ graph, with the origin (0,0) defined as the zero value for both the in-phase (I) component and the quadrature (Q) component. The sampling rate determines the number of discrete sampled IQ values. The higher the sampling rate, the more points that define the IQ trajectory. The IQ trajectory is ideally a smooth curve representing an infinite number of discrete sampled IQ values. In practice, there is always some finite number of sampled values, as defined by the sampling rate.
In hardware limitations, an IQ trajectory near the origin generates distortion in a corresponding output signal. Corrective signal processing of the sampled IQ values near the origin can improve the performance of the signal processing circuit. Conventional methodologies re-assign sampled IQ values that are near the origin to either a fixed distance away from the origin or to a default IQ value. In particular, sampled IQ values are compared to a minimum threshold value, and those sampled IQ values that are lower than the minimum threshold value are assigned to a minimum circular boundary about the origin or to a new default IQ value. In terms of the IQ trajectory and the corresponding IQ plot, there is one default IQ value associated with each quadrant of the IQ plot. The minimum threshold value defines a threshold region, which is typically the form of a box centered about the origin in the IQ plot. In this case, the threshold region is defined by the coordinates (+/−x, +/−x) on the IQ plot. The default IQ value for each quadrant is defined along the minimum threshold value at 45, 135, 225, and 315 degrees measured from the positive I-axis. These locations correspond to the corners of the threshold region.
FIGS. 1A and 1B illustrate an exemplary IQ trajectory and conventional approaches for revaluing IQ values near the origin. An IQ trajectory 10 is comprised of multiple sampled IQ values including a sampled IQ value 12, a sampled IQ value 14, a sampled IQ value 16, a sampled IQ value 18, and a sampled IQ value 20. In FIG. 1A, a minimum IQ value is defined by the threshold boundary value 24. The threshold boundary value 24 forms an outer perimeter of a threshold region centered about the origin 22. In simplified applications, any sampled IQ value that falls within the threshold region, such as the sampled IQ value 16, is to be revalued to a default IQ value. This default IQ value is conventionally assigned to be at the maximum threshold distance from the origin. A default IQ value is assigned for each quadrant within the IQ plot. In the configuration shown in FIG. 1A, the maximum threshold distance for the first quadrant is located at the point 26. Therefore, the default IQ value for the sampled IQ value 16 is the IQ value at the point 26. The maximum threshold distance for each quadrant is defined along the threshold boundary value 24 at 45, 135, 225, and 315 degrees measured from the positive I-axis. These locations correspond to the corners of the threshold region. Conventionally, only one default IQ value is selected per quadrant, which in this example is the IQ value 26. As such, any sampled IQ value that is less than the threshold boundary value 24, and therefore resides within the threshold region, is reassigned the default IQ value for the corresponding quadrant. For each quadrant in the threshold region, the default IQ value is the same regardless of where within the threshold region quadrant the sample IQ value is located. In general, this approach is referred to as a single-point push-out method, since for each quadrant, all sampled IQ values within the threshold region are “pushed-out” to the default IQ point.
In FIG. 1B, a minimum IQ value is defined by the minimum circular boundary 23. The minimum circular boundary 23 forms a perimeter of a threshold region centered about the origin 22. In simplified applications, any sampled IQ value that falls within the threshold region, such as the sampled IQ value 16, is to be revalued to a default IQ value. In this configuration, the default IQ value is a fixed distance away from the origin on the minimum circular boundary 23. Therefore, the default IQ value for the sampled IQ value 16 is the IQ value at the point 25.
Although the simplified approach of reassigning sampled IQ values near the origin aids in reducing distortion, using a fixed default IQ value leads to discontinuities in the IQ trajectory. Compare the IQ trajectory 10 in FIG. 1A with the default IQ value 26 and in FIG. 1B with the default IQ value 25. Such discontinuities result in transients in the frequency response.